1. Field of the Invention
This invention is related in general to the field of scanning interferometry and, in particular, to a new approach for correcting motion nonlinearities and other scanning errors occurring during interferometric measurements.
2. Description of the Related Art
Conventional scanning interferometry utilizes a light source, such as white light or a laser beam, to produce interference fringes at a light detector as the optical path difference (OPD) between a test surface and a reference surface is varied during a vertical scan. All measurement techniques based on phase shifting interferometry (PSI), vertical scanning interferometry (VSI, also referred to as white-light interferometry), combinations of VSI and PSI, phase shifting interferometry on-the-fly (PSIOTF), and lateral scanning interferometry (LSI, disclosed in Ser. No. 09/569,131) rely on an analysis of the interference between two beams of light. One beam (the object beam) is reflected from the sample; the other beam (the reference beam) is reflected from the reference mirror; and the two beams are recombined to create an interference pattern (the interferogram) at each scanning step. A detector (usually a CCD camera) registers the interferogram in a number of frames while the optical path difference (OPD) between the interfering beams is changing in a predefined fashion, which is realized either by moving the object, or by scanning the interferometric objective or the reference mirror at a preferably constant speed. The resultant shape of the sample object is calculated based on the intensity patterns in the interferograms and can be used to describe the height profile of the sample.
PSI is preferably used for measurements of smooth surfaces with small changes in profile (see K. Creath, xe2x80x9cTemporal Phase Measurement Methods,xe2x80x9d Interferogram Analysis, Institute of Physics Publishing Ltd., Bristol, 1993, pp. 94-140). VSI is generally used to measure smooth and/or rough surfaces with large interpixel height ranges (K. G. Larkin, xe2x80x9cEfficient Nonlinear Algorithm for Envelope Detection in White Light Interferometry,xe2x80x9d J. Opt. Soc. Am., A/Vol. 13, 832-843 (1996). The combination of VSI and PSI has been used, for example, to measure large steps with PSI precision (C. Ai, U.S. Pat. No. 5,471,303). The PSIOTF technique, which is a particular case of VSI and PSI combination, improves measurements of smooth surfaces in the larger height range (A. Harasaki et al., xe2x80x9cImproved Vertical Scanning Interferometry,xe2x80x9d Appl. Opt. 39, 2107-2115, 2000).
In VSI, interference fringes are localized only in a small region around the focus because of the low coherence source and/or the high numerical aperture of the microscope objective typically employed. While scanning through focus, fringes for different parts of the sample surface are produced and analyzed resulting in an unambiguous measurement of the object shape. As is well understood in the art, the height information from a low-coherence interferogram can be retrieved in many ways, such as, for example, by peak detection of the coherence envelope or fringe, by calculation of the centroid of the intensity signal, or by determination of the slope of the phase of the average wavelength. All these methods of analysis estimate the best vertical-scan focus position for a given pixel by sensing the coherence peak and utilize this information to determine the relative height difference between pixels (that is, a relative height profile of the test surface).
In PSI techniques, the interference fringes are examined only around a single focus position using a quasi-monochromatic light source such as a laser. PSI was introduced to the discipline of optics in 1974 from the telecommunications field (see J. H. Bruning et al., xe2x80x9cDigital Wavefront Measuring Interferometer for Testing Optical Surfaces and Lenses,xe2x80x9d Appl. Opt. 13, 2693-2703, 1974). Since then many applications of PSI have been developed for optics, resulting in a large number of reliable and robust algorithms (see, for example, P. Hariharan et al., xe2x80x9cDigital Phase Shifting Interferometry: a Simple Error-Compensating Phase Calculation Algorithm,xe2x80x9d Appl. Opt. 26, 2504-2505, 1987; and J. Schwider et al., xe2x80x9cDigital Wave-Front Measuring Interferometry: Some Systematic Error Sources,xe2x80x9d Appl. Opt. 22, 3421-3432, 1983). These algorithms produce phase measurements that may be ambiguous (because of so-called 2xcfx80 ambiguities) and therefore require further processing to remove the ambiguity by unwrapping the phase data. Because of this limitation, only objects with relatively small inter-pixel height differences can be measured using conventional PSI analysis. On the other hand, the advantage of PSI over VSI techniques is that PSI allows for more precise measurements.
The PSIOTF technique affords the high precision of PSI combined with the lack of ambiguity of VSI measurements. Accordingly, this combined technique is often utilized for determining the shape of smooth surfaces with moderate to large height differences (that is, surfaces with steep profiles). The procedure first involves finding a coarse focus position for each pixel using a VSI technique; then a PSI algorithm is applied to the intensity data collected at frames around this focus position to achieve a high precision measurement where the 2xcfx80 ambiguity has already been resolved by VSI. The PSIOTF technique can be used with a low-coherence light source or with a combination of both low- and high-coherence sources. In addition, the technique can be applied to each pixel individually or to groups of pixels in separate areas, as in the case of a stepped sample surface with separate smooth and flat regions.
All of these interferometric applications rely on accurate calibration of the scanning device used for changing the optical path difference (OPD) between the test object and the reference surface. Accordingly, these procedures cannot tolerate material departures from the calibrated condition. Scanner miscalibration, nonlinearities and vibrations affect the surface-profile measurements produced by PSI, VSI and PSIOTF algorithms by attributing an incorrect size to each scanner step, which in turn yields erroneous relative height measurements. Thus, the rate of change in OPD, normally referred to in the art as the xe2x80x9cphase step,xe2x80x9d needs to be well calibrated in order to achieve an accurate measurement. The most commonly used algorithms for the interferometric techniques used in the art require a predefined, nominal phase step which, once the scanner is calibrated, is assumed to remain constant along the whole scan for each measurement. However, this is not always the case and the errors in scanning speed influence the final result and need to be accounted for to achieve accurate measurements.
Calibration of the scanner is usually carried out as part of instrument maintenance and is assumed to remain unchanged during subsequent measurement runs. However, in fact the calibration may change, or the scanner can exhibit motion errors due to other influences such as friction, back-lash, etc. In such cases, these errors are carried forward into the measurement results in ways that depend on the type and magnitude of the phase-shift errors, and on the algorithm used to perform the interferometric analysis.
In view of the foregoing, it is recognized in the art that the advantage of high sensitivity afforded by optical interferometry is offset in part by its vulnerability to environmental influences, such as air convection, vibrations, scanner miscalibration and higher harmonics in the detected signal. A typical system operating at an average wavelength of 632 nm requires that scanning-step errors be confined to nanometer level; accordingly, all interferometric systems utilize some sort of vibration isolation, such as provided by air tables, or employ rather complicated active compensation circuits. This results in significant equipment cost and in limited mobility of such systems. In addition, these problems influence the range of applications and confine the use of interferometers to laboratories or selected in-field applications.
In practice, these errors cannot be easily corrected. They are also usually not repeatable from measurement to measurement, which adds to the difficulty of correcting them. Thus, eliminating or reducing the influence of these errors would be a great advance in the art and much work has been done to characterize errors associated with scanning perturbations. Improved algorithms have been developed to reduce sensitivity to error sources, but all state-of-the-art corrective techniques require intense calculations that greatly affect processing speed. For example, U.S. Pat. No. 5,953,124 describes a technique for correcting scanning nonlinearities using the three-dimensional interferogram produced by a completed vertical scan. The phase history determined within the coherence region of each pixel during the scan is temporally unwrapped to remove 2xcfx80 ambiguities, and overlapping temporal phase histories gathered from different pixels are connected to produce a measured phase history for the entire scan range. This measured phase history is then compared to the temporal phase change nominally produced by each scanner step to correct the height profile of the test surface. The approach produces corrected results that account for scanner nonlinearities, but it requires unwrapping of the phase data and complex post-scan data manipulation. These requirements prevent utilization of the method on-the-fly and further increase time, storage, and data-processing demands.
Another approach is disclosed in commonly owned copending application Ser. No. 09/875,638, hereby incorporated by reference, wherein interferometric measurements are carried out in conventional manner to produce a correlogram corresponding to successive scanner steps. An approximation of the actual scan-step size between frames is calculated from multiple-frame intensity data collected around the frame of interest using common irradiance algorithms. The scan-step size so measured is then used to perform standard PSI analysis, instead of the scanner""s nominal phase step. According to one embodiment of the invention, the phase step between frames is calculated directly utilizing a novel five-frame algorithm that produces an approximation of actual phase step for a given frame, rather than an average value of four steps around the frame. The method requires reduced data processing and can advantageously be applied xe2x80x9con-the flyxe2x80x9d as intensity data are acquired during scanning.
In both of the above cases, the phase step used to correct for nonlinearities and other scanning errors is an approximation of the actual phase step because of the multi-frame use of irradiance data required to carry out the inventions. In addition, to the extent that all prior-art approaches to phase-step correction utilize measurement correlograms, they are susceptible to shortcomings in the measurement data available for analysis (for example, overlapping coherence regions may not be available for total coverage of the scan range). Therefore, there is still a need for a more general and precise approach to correcting the errors introduced by nonlinearities and other sources in the scanner of an interferometer, so that a correct height profile can be determined on the basis of a corrected, actual scanner position history, rather than the calibrated, nominal scanning trajectory. This invention provides a solution to this problem by utilizing a reference signal dedicated to tracking the actual phase step occurring between scanning frames.
The primary objective of this invention is a method for monitoring the quality of the scan performed in an interferometric measurement and for correcting scanning errors produced by nonlinearities of the scanning mechanism and by other sources.
Another objective is an error-correction procedure that is independent of the characteristics of the light and optics used to perform the interferometric measurement.
Another goal is a technique that does not require phase unwrapping as an intermediate step to phase-step correction.
A final objective is a method that is suitable for implementation in conventional interferometric profilers and that is applicable for correction of PSI, VSI, VSI plus PSI, LSI or PSIOTF techniques.
Therefore, according to these and other objectives, the present invention consists of registering and storing an optical reference signal dedicated to providing a full history of the actual scanner motion, thereby allowing a determination of scanning errors at each step. The reference signal is independent of the light intensity information collected during the scan for measurement purposes. The concept may be implemented by utilizing an additional light source with the same scanner used for the measurement (with the same or a different detector), so that the OPD varies in synchronization of both the reference-signal and the data-collection procedures. Alternatively, a high temporal-coherence filter and/or a reduced numerical-aperture objective may be used with the same light source and optical path used for the interferometric measurement.
The important point is for the reference signal to provide intensity data that can be utilized to determine the exact position of the scanner at each step. To that end, the reference-signal interferometric set up is selected so as to optimize the precision with which this objective can be achieved. Thus, the reference signal may be acquired in the form of an interference signal at different or at the same wavelength as the profiler. The reference signal can be analyzed using any of several techniques used in the art to calculate the phase of the signal and/or analyze the shift of fringes during a scan. Thus, as would be apparent to one skilled in the art, these techniques include, without limitation, synchronous detection PSI, PSI with subtraction of ideal shift, average shift measurement algorithms, Fourier transform or other transform technique, correlation or convolution of data signal with a reference signal, zero-crossing, phase locked loop (pll), and any other technique used in telecommunication, electronics or signal processing.
In the preferred embodiment of the invention, the reference signal is obtained simultaneously with the measurement. but through the use of a different camera or point detector(s) than is used for collecting data for the surface measurement. The wavelength and the bandwidth of the reference signal are selected to have a coherence length sufficiently broad to cover the span of operation of the scanner. Thus, the use of a separate laser source is preferred, or a narrow bandwidth, filtered light from a halogen lamp. Furthermore, an additional aperture stop may be placed in the path of the light going to the reference signal detector to decrease the numerical aperture effect on the fringe envelope. The reference signal may reflect off the sample or some other object, like an additional mirror on the sample stage or the scanning device.
The phase step correction of the invention can be implemented during the measurement procedure with any type of measurement (VSI, PSIOTF, VSI+PSI, LSI or PSI) as a global calibration value or at each scanning position. An alternative option is to carry out the calibration with the reference signal before the measurement scan to determine the characteristics of the scanner, and to later use the calibration information either to control the scanner motion via a feedback loop or to correct each measurement step. Once error values have been calculated for each scan step, a look-up table may be constructed for the actual distances between frames acquired during the scan. This table can then be used to correct VSI, PSIOTF, LSI and PSI measurements. As a further option, the reference signal could be used in the feedback loop controlling the motion of the scanner.
Various other purposes and advantages of the invention will become clear from its description in the specification that follows and from the novel features particularly pointed out in the appended claims. Therefore, to the accomplishment of the objectives described above, this invention consists of the features hereinafter illustrated in the drawings, fully described in the detailed description of the preferred embodiment and particularly pointed out in the claims. However, such drawings and description disclose but one of the various ways in which the invention may be practiced.